Peaked Generative Learning Models Based on IQP Circuits

The field of Quantum Generative Models (QGM) has seen significant interest in recent years. In this work, we present a family of QGMs, that are based on IQP circuits with additional hardware friendly layers. The combination ensures efficient classical trainability, while still being out of reach for current circuit simulation methods. Moreover, verifiable supremacy experiments can be designed by training the model classically to learn circuits peaked around chosen bit strings which cannot be discerned using current classical simulation techniques, but can be easily determined using a quantum computer through measurements. We validate our approach through numerical simulations across multiple problem instances demonstrating various circuit designs with potential quantum advantage on circuits involving hundreds of qubits.